a Follow the instructions you are given in the book.
B
b Follow the instructions you are given in the book.
C
c Complete the given table with appropriate values.
D
d What can you say about the relationship between the coordinates of the dilated and the given triangles?
A
a See solution.
B
b See solution.
C
c See solution.
D
d The coordinates of the dilated triangle are the coordinates of the given triangle multiplied by the scale factor.
Practice makes perfect
a Let's start by drawing â–ł ABC. According to the given instructions we will draw vertex A at the origin and the vertices B and C at the whole-number coordinates.
To graph â–ł ADE that is twice large as â–ł ABC, we draw vertices D and E at the extensions of AB and AC. Moreover, the length of AD should be twice the length of AB and the length of AE should be twice the length of SegAC.
These are possible coordinates.
b Next, we will repeat the process from Part A two times. Let's label the second pair of triangles MNP and MQR using the scale factor of 3.
Finally let's use the scale factor of 4 to draw the third pair of triangles TWX and TYZ.
c In this part we will complete the given table with the appropriate values.
Coordinates
â–ł ABC
â–ł ADE
â–ł MNP
â–ł MQR
â–ł TWX
â–ł TYZ
A
(0,0)
A
(0,0)
M
(0,0)
M
(0,0)
T
(0,0)
T
(0,0)
B
(1,2)
D
(2,4)
N
(1,1)
Q
(3,3)
W
(0,2)
Y
(0,8)
C
(3,1)
E
(6,2)
P
(2,1)
R
(6,3)
X
(1,0)
Z
(4,0)
d Looking at the table we made in Part C we can see that in each case we can rewrite the coordinates of the dilated triangle as a product of the appropriate scale factor and the coordinates of the original triangle.
Coordinates
â–ł ABC
â–ł ADE
â–ł MNP
â–ł MQR
â–ł TWX
â–ł TYZ
A
(0,0)
A
( 2(0), 2(0))
M
(0,0)
M
( 3(0), 3(0))
T
(0,0)
T
( 4(0), 4(0))
B
(1,2)
D
( 2(1), 2(2))
N
(1,1)
Q
( 3(1), 3(1))
W
(0,2)
Y
( 4(0), 4(2))
C
(3,1)
E
( 2(3), 2(1))
P
(2,1)
R
( 3(2), 3(1))
X
(1,0)
Z
( 4(1), 4(0))
Therefore, we can assume that the coordinates of the dilated triangle are the coordinates of the given triangle multiplied by the scale factor.
